2 answers

You can turn your symbolic expression into a polynomial over a well-defined ring. Given the coefficients, i presume that they are floating-point numbers. Given the precision, the best "field" for that is RDF (if they had more digits of precision, you shoud have a look at RealField or RealBallField).

Just in case, if the coefficients could be described as rational or algebraic numbers, i would suggest to use them as coefficients within the correct polynomial ring so that you will get exact solutions.